报告人 ：陈浩（重庆师范大学数学科学学院  副教授）

报告人简介:陈 浩，毕业于威廉希尔足球官网，获理学博士学位， 现为重庆师范大学数学科学学院副教授，中国仿真算法专业委员会委员。主要从事微分方程数值解及数值线性代数研究，主持过国家自然科学基金及省级科研项目，在《J. Comput. Phys.》、 《Numer. Linear. Alge. Appl.》、 《BIT Numer. Math.》等计算数学重要刊物上发表科研论文20余篇。

报告题目：A dimensional splitting exponential time differencing scheme for multidimensional fractional Allen-Cahn equations

摘要：This talk is concerned with numerical methods for solving the multidimensional Allen-Cahn equations with spatial fractional Riesz derivatives. A fully discrete numerical scheme is proposed using a dimensional splitting exponential time differencing approximation for the time integration with finite difference discretization in space. Theoretically, we prove that the proposed numerical scheme can unconditionally preserve the discrete maximum principle. The  error estimate in maximum-norm  of the proposed scheme is also established in the fully discrete sense. In practical computation, the proposed algorithm can be carried out by computing linear systems and the matrix exponential associated with only one dimensional discretized matrices that possess Toeplitz structure.  Meanwhile, fast methods for inverting the Toeplitz matrix and computing the Toeplitz exponential multiplying a vector are exploited to reduce the complexity. Numerical examples in two and three spatial dimensions are given to illustrate the effectiveness and efficiency of the proposed scheme.

报告时间: 2020年11月3日20:30-22:30

报告地点: 腾讯会议ID：434 672 1949